Design Methodology for Screening Dynamic ... - ACS Publications

Ind. Eng. Chem. Res. 2010, 49, 9877–9886

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Design Methodology for Screening Dynamic Characteristics of Candidate Heat-Integrated Flowsheets Robert J. Brendel*,† and Prasad S. Dhurjati Department of Chemical Engineering, UniVersity of Delaware, Newark, Delaware 19716

Well-established design methods exist for generating candidate heat-exchanger networks (HENs), but there is a strong need for a methodology to screen for undesirable dynamic characteristics that are often observed in heat-integrated processes. In this paper, a simple transfer function-based method is developed that can assist in comparing dynamic behavior of candidate heat-integrated flowsheets. Use of the method allows the design engineer to determine the dynamic characteristics of the overall process shortly after identifying exchanger networks that satisfy the process heat balance. Mathematical development of the method is given, followed by explanations of its use. The basis of the method is developed in block-diagram format, making apparent the source of positive feedback that can result from adding heat integration to a process. Finally, the method is demonstrated on three candidate HENs for a simple process. The method allows for identification of dynamic characteristics that would not be determined through steady-state analysis alone. Background Heat-Exchanger Network Synthesis. Interest in energy efficiency in the process industries has generally increased over the last few decades, with peaks and valleys following the cost of energy. Lately, concern over greenhouse gas emissions and climate change has raised the profile of energy efficiency again. One of the methods available to industry for designing energyefficient processes is to incorporate heat integration, meaning using process streams as heat sources and sinks as much as possible, minimizing the use of utilities. Heat integration began to be systematically applied in industry following the work of Bodo Linhoff and many co-workers in developing the pinch analysis technique. Initially applied to synthesis of heat recovery networks for new process flowsheeting, it was later extended to be applicable to retrofits. The intuitive approach to heat recovery, coupled with the relative ease of calculation, popularized the application by the early 1980s. (See the work of Linhoff and Vredeveld1 for a useful introduction and history of pinch technology.) Process-to-process heat integration changes the dynamic characteristics of a process, compared to using process/utility heat exchange exclusively. Conventional wisdom early on decided that the changes arising would generally have ill effects, making the process more difficult to startup and control; anecdotal professional experience of the authors confirms industrial conventional wisdom. Heat-Exchanger Network Dynamics. There is a significant collection of work in the literature dealing with dynamics and control of a heat-exchange network (HEN) itself. Since most of the HEN design techniques mentioned above do not deal with variations from the nominal steady-state point, the aspect receiving the most attention is the flexibility of the HEN to operate at conditions away from the nominal steady-state conditions (which every installed HEN must do eventually). Morari and co-workers have defined a “resilience index”2 and two “resilience targets”,3 with regard to the ability of a designated HEN to deal with changes in inlet and target * To whom correspondence should be addressed. E-mail: [email protected]. † Current address: Honeywell Process Solutions, Beijing 100125, PRC.

temperatures. The index and targets are useful for detecting and avoiding potential bottlenecks in HENs that may prevent it from operating within acceptable limits when not at the design conditions. Kotjabasakis and Linnhoff4 incorporated costs into the flexibility analysis, developing “sensitivity tables” to assist in the effort. Later work considered the structure or topology of the HEN itself, such as the locations of split streams and mixes, as well as exchanger bypass locations, in the flexibility and contollability analyses, incorporating dynamics explicitly. Mathiesen et al. considered both steady-state and dynamic considerations in the HEN synthesis problem, with special attention given to locations of exchanger bypass streams.5-7 Varga and Hangos8 incorporated the cell model in their effort to use the resulting signaldirected graphs to elicit qualitative information about the network. Papalexandri and Pistikopoulos9,10 also used graphs, considering nodes as decision points in a mixed-integer nonlinear programming problem. Dynamics were considered in a systematic procedure that considered all potential matches and flow arrangements. Glemmestad et al.11 explicitly addressed control aspects of the HEN, maintaining target temperatures in the presence of inlet temperature disturbances while minimizing utility consumption. Boyaci12 et al. developed optimal control schemes for manipulating exchanger bypass flows, with the optimal flows defined as those with minimum deviations from the target stream temperatures. Stream flow disturbances were considered along with inlet temperature disturbances. Uzturk and Akman13 considered the retrofit problem in which bypass streams are to be added for flexibility. Candidate HENs were screened based on the resiliency and estimates of closed-loop interactions. Overall Heat-Integrated Processes. Studies of the dynamics of heat-integrated processes reported in the literature have typically been case studies, as opposed to development of insights and analysis methods. The general topic of process dynamics is rich and well-developed, and the techniques developed are used for analysis of specific heat-integrated processes. Luyben has published much work in this area, usually with applications in distillation. He explored steady-state design, including control considerations, with Tyreus14 and Chiang.15-17 With Ding,18 he investigated via simulation the dynamics of a

10.1021/ie901399f  2010 American Chemical Society Published on Web 09/08/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 20, 2010

heat-integrated complex distillation system that he had proposed with Cheng,19 based on steady-state energy consumption considerations. Luyben and Ding reported that only at high purities was the column control significantly more difficult for heat-integrated system versus the conventional system. Luyben also considered some general aspects of dynamics of heatintegrated distillation columns in a book chapter.20 Koggersbol et al.21 considered the dynamic effects of heat integration on a single column via a heat pump, and they showed that a base-case integration scheme changed the column to openloop unstable. Morud and Skogestad22 showed the similarities that exist between the dynamic effects of material recycle streams and heat integration: both have a tendency to introduce positive feedback, generally decreasing stability and introducing the possibility of complex dynamics. The design methodology developed in this paper shows this positive feedback effect in block diagram format. This paper is arranged as follows. The next section introduces the flowsheet screening method developed recently and describes the problem that it is intended to solve. The mathematical formulation of the method then is outlined, such that it allows description of a heat-integrated process in familiar blockdiagram form, separating the exchanger network from the rest of the process unit operations. Next, use of the method to screen candidate exchanger networks for a simple reactor/separator process is demonstrated. The final section offers conclusions. Introduction to the Flowsheet Screening Method Typical Design Methods for Heat-Integrated Processes. Continuous heat-integrated processes are typically designed in two steps, as outlined in Douglas.23 First, the steady-state material and energy balances are generated, which defines the process streams and required duties (what we call the process “skeleton”). A heat-exchange network (HEN) then is constructed to satisfy the heat balance while minimizing capital and operating costs. Process complexity is considered only indirectly, through the consideration of installed cost, in that more-complex solutions will generally have more exchangers. The HEN resulting from steady-state design tools generally results in an overall process that introduces new process interactions that may present difficulties for operability and control of the plant. When this is recognized by the designer as a possibility, several candidate HENs may be generated for consideration, instead of simply accepting the solution with the apparently lowest cost either by inspection, through steady-state analyses, or, in a few cases, by dynamic simulation. These candidates are then evaluated for likely difficulties in startup, operation, or control. However, process complexity may prevent the design engineer from estimating overall plant dynamics merely by inspection, from experience with similar units, or through the use of steady-state design methods. This paper introduces a method for assessing overall process dynamics early in the design stagesat the HEN generation stage. It is assumed that the process skeleton is relatively fixed, and the designer has one or more candidate HENs to consider. The method will help the designer assess the approximate dynamic character of the overall unit if a candidate HEN is installed. [Since the dynamics are expressed here in terms of (necessarily linear) transfer functions, the results of applying the tool will be valid in the region of the steady-state design point. Abnormal situations such as startup/shutdown or emergency cases cannot be investigated using the method developed here.] Evaluating Dynamic “Character”. One important aspect of process dynamics is the effects of disturbances. These are

typically investigated based on knowledge of the process being designed, and the engineer’s experience, likely disturbance sources, and their magnitudes are identified. The designer also chooses the temperatures most critical in the process and focuses attention on how these will be affected by the disturbances. These important points may be entry points into unit operations, such as reactor inlet temperatures, or they may be other internal streams that significantly affect safety or product quality, such as reboil return temperatures or column overhead temperatures. The results of this analysis can help define the load any control system will be called upon to reject, with the smallest disturbances propagated being desirable. One tool that is helpful in this analysis is the relative disturbance gain.24 Another characteristic important for operation and control is the level of interactions among important process variables. For evaluation of heat-integrated flow schemes, the focus is naturally on interactions between temperatures of particular interest. The magnitudes of these interactions have some bearing on control system input/output pairing choices. Developing this information early in the design phase may help to concentrate quickly on a heat recovery structure that is likely to perform well. The condition number25 is commonly used as an indication of the magnitudes of interactions. Note that these topics can be investigated, to some extent, using only steady-state (zero frequency) models.26 In fact, a steady-state analysis may be informative enough to select among candidate flow schemes in some cases, and it should be performed any time that questions arise regarding the dynamic character of the heat-integrated unit. However, important information may be left undiscovered in the absence of explicitly accounting for dynamics. As shown in the simple examples included here, some flow schemes that appear to have a similar “flavor” at steady state may diverge as frequency increases, because of inherent time constants of the various equipment. Thus, the method described here can play a useful role in helping to select among candidate HENs based on dynamics, or confirming that a candidate HEN will not give an unpleasant surprise, relative to the dynamics, later in the design phase. Method Development There are several well-established tools to assist the design engineer in answering where best to transfer heat within the process while satisfying the duties prescribed in the material and energy balance. The goal is to maximize use of “free” process heating and cooling, avoiding the consumption of relatively expensive utilities. Perhaps the best-known of these methods is pinch analysis, which was developed largely by Linhoff and co-workers. The pinch technique allows the designer to intelligently determine targets before beginning the work of deciding how and where to recover process heat. The task of meeting the targets is typically performed by generating a heatexchange network (HEN) diagram. Consider the simple process flow diagram (PFD) of Figure 1 for a process consisting of a reactor and separator. This PFD represents the steady-state design energy balances satisfied with a hot utility (hot oil) for every heating load, and a cold utility (cooling water) for every cooling load: there is no recovery of any process heat, and, therefore, no heat integration. The HEN diagram for this process is shown in Figure 2, where the four exchangers are represented as matches among the streams following conventions used in pinch analysis. Note that all of the stream initial points are either entries from the process boundaries or exits from a unit operation. Similarly, all the final (or “target”) points are either exits from the process


Figure 1. Case 0: the example process with no heat integration. Duties are given in units of MMBtu/h.

individual heat exchangers in the network must be estimated. Methods have been published for estimating the dynamics of heat exchangers based on design fluid properties and conditions, along with physical details of the exchangers such as the number of tubes and passes.27 Finally, the dynamics of unit operations outside the HEN must be incorporated if they are not significantly slower than those of the exchangers proposed. A heat exchanger with two single-phase fluids and constant flow rates is a two-input, two-output system. The independent inputs are the two inlet temperatures, while the dependent outputs are the two outlet temperatures. If the dynamic effects on the outputs caused by changes in the inputs are linear, they may be represented as transfer functions. If the effects are nonlinear, they may be linearized to obtain transfer functions. Figure 3 shows these transfer functions as four arrows leading from inputs to outputs for one of the exchangers. Transfer functions gA011(s) and gA051(s) represent the dynamic effects changes in T1,i cause in T1,f and T5,f, respectively; effects of T5,i on T1,f and T5,f are represented by gA015(s) and gA055(s). These four transfer functions are the elements in the matrix for exchanger A0 in the example PFD:

[ ] [

T1,f(s) gA011(s) gA015(s) ) T5,f(s) gA051(s) gA055(s)

Figure 2. Base network diagram. Duties shown are given in units of MMBtu/h.

boundaries or entries into a unit operation. [HEN diagrams are typically used to aid in identifying matches between process streams that will increase overall heat recovery and reduce usage of utility fluids. For this reason, they often do not explicitly show utility fluids in the network. We have included them on the diagrams shown here since our focus is on the dynamics of the network and the overall process, and the effects of changes in the utility fluids can be of interest in these problems.] Construction of HEN Temperature Dynamics by Path Analysis. For units in the process industries, the temperatures of particular bearing on operation and control of a plant being designed are commonly feed temperatures to process unit operations, or product temperatures. Note that, in both cases, the stream final temperature is the point of interest. Changes in the initial stream temperatures may be either disturbances or results of controller manipulations. Naturally, their dynamic effects on various final temperatures will be dependent on the structure of the HEN; therefore, the engineer may wish to review the estimated dynamics of candidate HENs early in the design phase, so that those resulting in units with poor controllability and operability are abandoned as soon as possible. The layout of the HEN diagram lends itself to construction of dynamics via path analysis. To accomplish this, temperature dynamics of

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][ ] T1,i(s) T5,i(s)

(1)

Transfer functions for the overall HEN temperature dynamics can be constructed via path analysis by assembling the dynamics between a final temperature of interest and all initial temperatures considered likely to be a source of disturbances or a possible control manipulated variable. Generating HEN dynamics via path analysis treats the HEN diagram as a linear block diagram, where each arrow represents a transfer function block. Establishing the HEN dynamics of the example process was straightforward, since there is no heat exchange between process streams, and every path from an initial temperature to a final temperature encounters only one exchanger. As a more-complex illustration of path analysis, consider instead the HEN shown in Figure 4, in which the effects of T3,i on T2,f are constructed. Working backward from T2,f, first the effects on T2,f of changes in the intermediate temperature T2,a are expressed as T2,f(s) ) gc(s) T2,a(s). Similarly, we find T2,a(s) ) gb(s) T1,a(s) and so on backward to T3,i. Representing the dynamics of the entire route from T3,i to T2,f as T2,f(s) ) Gh2, 3(s) T3,i(s) yields the product Gh2, 3(s) ) gcgbga(s). In the case of multiple paths from an initial temperature to a final temperature, the total effect is the sum of those traced along all paths. This is illustrated in Figure 5 in which there are two routes by which changes in T4,i affect T2,f. The transfer function for the first route is simply the dynamics for that element of exchanger D: T2,f(s) ) ga(s)T4,i(s)

(2)

For the second, longer route that passes through all four exchangers, the transfer function is T2,f(s) ) gfgegdgcgb(s)T4,i(s)

(3)

The transfer function that captures both of these routes, and, thus, completely defines how T4,i affects T2,f is Gh2,4(s) ) ga(s) + gfgegdgcgb(s)

(4)

The case of loops is treated the same as feedback loops in conventional block diagrams. [Some authors refer to loops in HEN diagrams as “paths”. We have chosen not to follow this;

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Figure 3. HEN diagram showing 2 × 2 transfer functions for Exchanger A0.

Figure 4. HEN diagram showing the path between one one initial temperature and one final temperature.

Figure 6. HEN with one loop.

Solving for T1,a(s) and substituting gives T1,f(s) )

Figure 5. HEN with multiple paths between initial temperature T4,i and final temperature T2,f.

instead, here, “path” means an achievable route from one point to another, following the forward flow of the process streams. In addition, here, “loop” follows block-diagram conventional usage.] The HEN in Figure 6 has a loop as shown, with individual exchanger dynamics in the form of Laplace transforms represented by arrows. The effect that changes in T1,i have on T1,f are obtained by working backward from T1,f to T1,i through intermediate temperature T1,a: T1,f(s) ) gb(s)T1,a(s) T1,a(s) ) ga(s)T1,i(s) + gfgegdgc(s)T1,a(s)

gbga T (s) 1 - gfgegdgc 1,i

HEN Extension for Variable Flow. Process and utility stream flowrates are commonly used as manipulated variables, so that they are important when considering the overall plant dynamics. This section describes how the HEN diagram representation may be extended to include flows. In the flowsheet in Figure 1, if the flow of hot oil to the exchanger A0 may be manipulated, it is a potential control input. Figure 7 shows how this may be incorporated into the HEN diagram by considering each variable flow as another process stream to be included in the match. (Therefore, a match could include up to four components, if both flows are nonconstant.) Dynamic effects of changes in the flow rate on the exchanger outlet temperatures are represented again as arrows on the HEN diagram. Changes in the flow rate of hot oil will affect both outlet temperatures, increasing the dimension of the overall exchanger from a 2 × 2 to a 3 × 2 system. (For incompressible flow and constant fluid properties, the inlet and outlet flow rates are identical, so no effect is shown between F5a,i and F5a,f, and, for the sake of simplicity, the arrows are shown as originating from either one.) In some cases, variations in flow of one stream to a heat exchanger can affect the flow of the other stream. An example


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Figure 9. HEN illustrating bypass (Stream 1 around Exchanger C) and total flow (Stream 3) effects.

Figure 7. Extension of the base network diagram to include effects of varying Stream 1 flow.

rate of Stream 1 through exchanger C is adjusted with a bypass, while the total flow of Stream 3 is adjusted. When changes are made to the Stream 1 bypass flow around Exchanger C, the flow rate of Stream 1 through Exchanger A is unaffected, so the representation for Exchanger A does not include a connection to F1. Although the final temperature of Stream 1 is affected by the change in bypass flow of Stream 1 around Exchanger C, the effect is transferred through changes in the upstream temperature, instead of through the change in flow directly. Contrast this situation with that for Stream 3. When the total flow through Exchanger C is modified, the flow of Stream 3 through Exchanger B also changes, so the match for Exchanger B must include a connection to F3. Block Diagram Representation By definition, the HEN represents the process between the initial and final temperature points. Thus, the HEN transfers dynamic effects from the initial to final stream temperatures. When these temperature points are collected in vectors, the approximate HEN temperature dynamics may then be written in vector-matrix form. The example process shown in Figure 1, for example, is represented as Ti ) [T1,i T2,i T3,i T4,i T5,i T6,i T7,i T8,i ]T Tf ) [T1,f T2,f T3,f T4,f T5,f T6,f T7,f T8,f ]T

(6)

Tf(s) ) Gh(s)Ti(s)

(7)

Figure 8. HEN for the case of F5a,i affecting F1,f.

would be in increase in steam flow to a total reboiler, causing an increase in boilup flow for the column. In that case, the exchanger is a 3 × 3 dynamic system:

[ ][

T1,f gh1,1 gh1,5 gh1,F5a T5a,f ) gh5a,1 gh5a,5 gh5a,F5a F1 ghF1,1 ghF1,5 ghF1,F5a

][ ] T1,i T5,i F5a,i

(5)

Representation of the match would include four joined circles and an additional transfer function; the third column of the transfer function matrix in eq 5 is shown as arrows in Figure 8. Note that, for a varying total flow rate, each exchanger through which the stream passes will include a connection to that flow variable. For a manipulated bypass flow, however, only a single exchanger will have a connection to the flow variable; the downstream exchangers in the path do not experience any flow change and only interact through temperature changes. Both cases are illustrated in Figure 9. The flow

As noted in the Method Development section, HEN initial points are either outlets from unit operations or entries from the process boundaries. HEN final points are either feeds to unit operations or exits from the process boundaries. Thus, the process skeleton transfers effects from at least a subset of HEN final points to initial ones. Following the vector notation, the approximate (linearized) temperature dynamics of the process skeleton may then be written as Ti(s) ) Gp(s)Tf(s)

(8)

As the previous section extended the HEN diagram to include varying flows, the vectors and matrices of eqs 6-8 can also be extended to include, in the analysis, dynamics due to varying flows. In the example process, the flow rate of Stream 5 varies as

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vector u, and the disturbances in vector d, these selections may be expressed in vector-matrix notation as

Ti ) [T1,i T2,i T3,i T4,i T5,i T6,i T7,i T8,i F5,i ]T Tf ) [T1,f T2,f T3,f T4,f T5,i T6,i T7,i T8,i F5,f ]T

y ) CTf u ) DTi d ) ETi

(9) where, for incompressible single-phase fluids, Ff ) Fi at every instant in time. For the example process, the matrix Gh is constructed by tracing the path (if any) through the HEN from every final point back to every initial point: Gh ) Gh11 )

Gh12 )

Gh21

)

) Gh22

[

Gh11 Gh12 Gh21 Gh22

[

]

]

ghA01,1 0 0 0 ghB02,2 0 0 0 ghC03,3 0 0 0 ghD04,4 0 0 0 ghA01,F5 ghA01,5 0 0 0 ghB02,7 0 0 0 0 ghC03,8 0 0 0 0 ghD04,6 0 0 0 0

[

[ [

]

ghA05,1 0 0 0 ghD06,4 0 0 0 ghB07,2 0 0 0 ghC08,3 0 0 0 0 0 0 0 ghA05,F5 ghA05,6 0 0 0 ghD06,6 0 0 0 0 ghB07,7 0 0 0 0 ghC08,8 0 0 0 0 0 0 0 0 1

]

]

(10) As noted above, for this simple example with no process-process heat exchange, each HEN path consists of only a single transfer function associated with the dynamics of one particular exchanger. In general, Gh will be an invertible transfer function matrix with no zeros in the diagonal. The process skeleton matrix Gp for the example has only three nonzero entries. One entry represents the propagation of temperature effects from the reactor inlet (T1,f) to the reactor outlet (T2,i). The two other transfer functions are for the temperature dynamics of the separator: one for the inlet to the vapor (T2,f to T3,i) and another to the liquid (T4,i). These individual transfer functions are assigned to elements of Gp as follows: Gp(2, 1) ) gpRxr2,1 Gp(3, 2) ) gpSep3,2 Gp(4, 2) ) gpSep4,2

(12)

In the example process, consider that the controlled variables will be the reactor inlet temperature (T1,f) and separator vapor final temperature (T3,f). Also consider that the likely manipulated variables are the total flow rate of hot oil to exchanger A0 (F5 ) T9) and the flow of cooling water to the separator vapor cooler (T8,i). The only anticipated disturbance is the feed supply temperature (T1,i). The input/ output selection matrices become

[ [

1 0 0 D) 0 E ) [1

C)

0 0 0 0 0

0 1 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 1 0 0

] ]

0 0 0 1 0]

(13)

The block diagram in Figure 10 captures these relationships. Representing the heat-integrated process in this manner also shows the source of the positive feedback effect that arises from heat integration, which is an effect that has been noted by several previous researchers. The heat-integrated plant has been represented as two interacting sectionssthe process skeleton and the HENscorresponding to the typical process design sequence. The dynamics of the overall process, which consists of the HEN and the skeleton, may be expressed in terms of the input/ output equation y ) Gu + Gdd

(14)

G ) C(I - GhGp)-1GhDT Gd ) C(I - GhGp)-1GhET

(15)

where

In some process units, it may be desirable to designate an initial temperature point as an output to be tracked. One example

(11)

Generally, the process matrix will be sparse and will not be invertible. Elements of the matrix Gp represent the process skeleton, and, in the typical design procedure as outlined by Douglas,23 they will usually be the same for each candidate HEN under consideration. Stream numbering may change from case to case, but the process elements will remain the same. Typically, the controlled variables in a heat-integrated process (the outputs) will be a subset of the final temperatures, for example, a reactor inlet temperature or a product exiting the problem scope. Similarly, the manipulated and disturbance variables (inputs) will be a subset of the initial temperatures or flow rates. If the outputs are collected in vector y, the inputs in

Figure 10. Block-diagram representation of a heat-integrated process. Table 1. Stream Properties for the Example Process stream

Ti [°F]

Tf [°F]

F [klb/h]

effective Cp [Btu/lb °F]

1 2 3 4 CW oil

100 222 150 150 75 350

200 150 100 200 105 250

90.1 90.1 36.0 54.1 varies varies

1.1 1.3 1.1 0.53 1.0 0.48


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Figure 11. Case 1: Example process with FEHX. Duties are given in units of MMBtu/h.

might be when a reactor outlet temperature is controlled instead of a reactor inlet temperature. The methods described above can be extended to include this case. The solution is to insert in the process a dummy unit operation and dummy exchanger, both of which are static unity gains. This introduces a new stream into the problem and increases the dimensionality by one, but allows for an initial point to be selected as an output. After Gh and Gp have been identified, the plant dynamics of the candidate HEN in the overall process can be evaluated quickly using several established multivariable analysis tools. The problem of screening candidate flowsheets based on dynamic character is then reduced to constructing the two matrices containing the dynamics of the individual sections. Illustrative Example Use of this tool is illustrated in the analysis of a simple process involving a plug-flow reactor and a separator. Cooling water and hot oil are available utilities. Stream details are shown in Table 1. The nonintegrated base case is designated Case 0 (see Figure 1). A commonly used form of heat integration for reactor/ separator systems is to include a feed/effluent heat exchanger (FEHX), as in Figure 11, which is designated as Case 1 here. More-extensive integration is investigated through pinch analysis; the composite curves for this process are shown in Figure 12, with a 20 °F pinch constraint. These curves suggest the stream pairings shown in the flow diagram of Figure 13, which is designated as Case 2. Thus, three candidate flowsheets are defined: Case 0, with no integration and maximum utilities consumption; Case 1, with simple integration including feed/ effluent exchange around the reactor; and Case 2, with extensive integration developed by established steady-state design methods. Some process details are given in Table 2. The minimum cold and hot utilities required for the chosen approach temperature are 0.8 and 1.8 MMBtu/h, respectively. Case 2 comes closest to achieving these targets at the cost of an increased number of exchanger shells, relative to Cases 0 and 1. The question of input and output selections remains. Here, there are two temperatures that are particularly important, and they are chosen to be the outputs: the reactor inlet temperature and the separator inlet temperature. The manipulated variables (inputs) are the flow rate of hot oil to the feed heater upstream of the reactor (Exchanger A) and the flow rate of cooling water supplied to the separator cooler exchanger (Exchanger B).

Figure 12. Composite curves for example process; 20 °F pinch.

Each exchanger is a shell and tube exchanger, designed using default methods in UniSim Design. First-order laplace transform models were obtained for exchanger temperature dynamics from simulated step changes in the dynamic UniSim model. The reactor and separator were treated similarly. Overall process dynamics for the various cases were investigated by constructing the Gh and Gp matrices as described above, then evaluating them numerically for a range of frequencies. First, the condition number will give a measure of the interactions to be expected between the chosen outputs when the input is varied. As shown in Figure 14, the nonintegrated Case 0 shows the smallest interactions between the reactor inlet temperature and the separator inlet temperature, indicating that the two outputs will be the easiest to control independent of each other in the absence of heat integration. The interactions do not increase much with the addition of the feed/effluent exchange in Case 1. The extensive heat exchange network in Case 2, however, introduces significant interactions between the two points of primary interest, which is apparent from the flowsheets. The relative levels of interactions hold for all frequencies of interest. Disturbance effects were investigated by numerically evaluating the Gd matrix. The upper plot in Figure 15 shows the open-

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Figure 13. Case 2: Example process with extensive heat integration. Duties are given in units of MMBtu/h. Table 2. Case Design Comparisonsa case

hot utility [MMBtu/h]

cold utility [MMBtu/h]

HX shells

0 1 2

11.4 4.4 2.8

10.4 3.4 1.8

4 5 8

a Minimum cold and hot utilities are 0.8 and 1.8 MMBtu/h, respectively.

Figure 15. Magnitude of effects of disturbance variables on reactor inlet temperature.

Figure 14. Condition number for candidate flowsheets.

loop magnitude of a feed initial temperature disturbance on the reactor inlet temperature; the lower plot shows how the reactor inlet temperature is affected by changes in the supply cooling water temperature to the separator inlet cooler. The same two disturbance effects on the final separator vapor temperature are shown in Figure 16. The existence of feed/effluent exchange around the reactor results in larger steady-state feed temperature disturbances propagated to the reactor inlet for both integrated cases, relative to the nonintegrated flowsheet (Case 0). The relative order of the steady-state disturbance magnitudes follows the same order as the amount of heating duty supplied by the utility hot oil. At frequencies of >10-3 s-1, the disturbance magnitude for Case 2 decreases below those of the less-integrated cases, which is a

development that could not have been predicted using steadystate analyses alone. This same change in relative disturbance magnitudes is observed in the effects of initial feed temperature on the separator inlet temperature. There is no effect of cooling water supply temperature on the reactor inlet for Cases 0 and 1, since there is no path in the overall process to deliver them. In Case 2, however, changes in cooling water temperature can affect the reactor inlet temperature via multiple paths originating at Exchangers F2 and H2. Finally, the relative magnitudes of cooling water supply temperature disturbance effects on the separator inlet temperature follow the trend of the cooling duty supplied by cooling water. The less-integrated cases are more susceptible to variations in cooling water for all frequencies. The magnitudes of the steady-state disturbance effects can be demonstrated in traditional design simulations. The varying relative magnitudes at frequencies of >10-2 s-1 were investigated via dynamic simulation using Honeywell’s UniSim Design R390 software. The feed temperature was changed from 100 °F to 125 °F after 60 s. After 30 s, the feed temperature was decreased to 75 °F, and it was returned to 100 °F after another 30 s. During


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Thus, although the steady-state analysis suggests that the increased heat integration of Cases 1 and 2 over the nonintegrated Case 0 would result in larger temperature disturbances and a more difficult control problem for the two inputs chosen, evaluation of the dynamic effects presents a different picture, depending on the frequency of disturbances expected for operation of the unit. Summary

Figure 16. Magnitude of effects of disturbance variables on separator vapor final temperature.

A representation of heat-integrated process dynamics as two separate interacting sections has proven to be an effective tool for analysis of the overall process dynamics early in the design stage. The process decomposition is logical in that it follows the typical work sequence of process design steps. The traditional HEN representation has been used for generation of the network dynamics Gh matrix; the graphic HEN representation has been extended to include variable flow effects. Dynamic characteristics of a candidate heat-integrated flowsheet can be evaluated using the methodology developed here, providing the designer with insights into the nature of the overall system that results from application of the candidate heatexchanger network. Those candidates that give rise to undesirable dynamic effects can be modified or abandoned early in the design process, improving engineering efficiency. Acknowledgment The authors thank UOP, a Honeywell company, for partial support of this research. Nomenclature

Figure 17. Simulation results for a series of changes in feed temperature.

Btu ) British thermal unit d ) vector of disturbance variables Cp ) stream mass heat capacity F ) stream flowrate F ) vector of stream flowrates Gh ) matrix of heat-exchanger network dynamics Gp ) matrix of fixed unit operation dynamics I ) the identity matrix klb/h ) mass flow, in thousands of pounds per hour MMBtu/h ) energy rate, in millions of Btu per hour s ) Laplace variable T ) stream temperature T ) vector of stream temperatures u ) vector of input variables y ) vector of output variables Subscripts

this simulation, the temperature controllers for the reactor and separator inlets were set to manual mode; all other controllers were in automatic mode. The effects of the feed temperature changes are shown in Figure 17. Clearly, the magnitude of the disturbance propagation at the reactor inlet is largest for Case 0 in this test, although that case shows the smallest steady-state magnitude. For the separator inlet temperature, the magnitude of the disturbance is greatest for Case 1 for the frequency of the feed temperature variation. The speed of the disturbance propagation varies among the cases, as would be expected from the analyses done above. The rate of temperature change for both the reactor and separator inlets is greatest for Case 0 and slowest for Case 2. The slower rate of change would indicate an easier control problem to address for the important process variables in this example.

i ) stream initial condition at origin f ) stream final condition out ) stream final condition at terminus

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ReceiVed for reView September 7, 2009 ReVised manuscript receiVed June 30, 2010 Accepted August 23, 2010 IE901399F

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